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Friday, March 30, 2012

Charles Dodgson is a genius

This article, "Bracket Through the Looking Glass," is from the Wall Street Journal, which is usually far too smart for me to understand - or at least that's the excuse I give for not reading it.

The article summarizes a plan from "Alice in Wonderland" author Lewis Carroll, pen name of mathematician Charles Dodgson.

From writer Rachel Bachman, who admirably explains matters:The monograph, "Lawn Tennis Tournaments, The True Method of Assigning Prizes with a Proof of the Fallacy of the Present Method," is just about what it seems to be: a proposal for a better way to conduct a sports tournament...

Carroll wrote that he got the idea after hearing the "lamentations" of a lawn tennis player who told Carroll he'd been beaten early in the tournament, and had then suffered the "mortification" of watching a clearly inferior player take home second prize, rather than he.

The trouble, Carroll realized, was that the randomness of the draw, coupled with the single-elimination format, didn't always result in a fair trip through the draw for the best players...

In Carroll's system, the draw would be assigned alphabetically with no attention paid to skill. If a player won his first-round match, Carroll proposed, he would advance to play other winners. But the losers would not be eliminated. Rather, they would move on to play other losers. The only way any player could be eliminated, he wrote, was after they had amassed three "superiors." He defined a superior as any player who has beaten you, or any player who has beaten a player who has beaten you.

In a nutshell: ... Losing a single match to anyone won't kill you, so long as you keep winning. The only way to be knocked out is if the player who beats you drops two more matches along the way.

This is an outstanding idea, filled with wisdom.

How do you measure quality? By success, yes, and also by the ability not to lose to an inferior competitor. A champion produced by this tournament format would be considered, bar none, the true titleholder in her or his field.

The only negative would be that the tournament would last a while. I'm willing to sacrifice duration in support of determining a true champ.